That included not just getting dental records but going to her apartment in Nassau, police said.

"We'll get her DNA sample, we'll go to her apartment, grab DNA and try to match up DNA," Skopek said.

But detectives still have another mystery -- what she was doing at the house, whose back looks onto the South Oyster Bay and was sheared off during Sandy. A neighbor said the house, covered with boards and tarp, had been a recent estate sale.

Some in the neighborhood speculated the woman was a squatter, but Skopek disagreed.

It's been challenging finding answers, the detective said, because a lot of the homes nearby remain vacant post Sandy, including the houses adjoining the one in question.

Skopek said he saw high school students get out of a bus nearby, an indication that people have walked by the house, but no one had seen the body until the sound of water spilling from the house attracted contractors working next door.

Chest-high or so hedges bordered the front yard, and 4 feet from them was the body, lying under an overhang of the house, the detective sergeant said. The woman was wearing a dark-colored, three-quarter-length coat and dark pants and shirt, he said.

"We're going back to that neighborhood," Skopek said. "Hopefully, we can dig up something. Maybe somebody had a home video there or surveillance camera."